Modeling and numerical analysis of the effect of dissociation/recombination of water molecules on the transport of salt ions in diffusion layer

Introduction. The paper presents a theoretical study on binary salt ion transport considering the water dissociation/recombination reaction. The work objectives are as follows: to build a mathematical model; to develop an algorithm for the numerical solution to the boundary value problem corresponding to the mathematical model; to work out the similarity theory including the transition to a dimensionless form using characteristic quantities; to determine a physical meaning of trivial similarity criteria; to find nontrivial similarity criteria; to build and analyze the volt-ampere characteristic (VAC).

Materials and Methods. The theoretical study and numerical analysis of the transport of binary salt ions consider the dissociation/recombination reaction of water. In this case, the heat transfer equation and the mathematical model of electrodiffusion of four types of ions simultaneously (two salt ions, as well as ????⁺ and ????????⁻ions) in the diffusion layer of electromembrane systems with a perfectly selective membrane are used. For the first-order differential equations, a singularly perturbed boundary-value problem is set. In the equation for the electric field, the right side is independent of the intensity. In the numerical solution to the digitized system of equations by the Newton-Kantorovich method, this causes the stability of the method. In this regard, the boundary-value problem is reduced for numerical solution: a transition to a system of the second-order equations is provided, and the missing boundary conditions for the electric field strength are calculated.

Research Results. A new mathematical model, a numerical algorithm to solve a boundary value problem, and software are developed. A numerical analysis is carried out, and fundamental laws of the transport of salt ions are determined considering the dissociation/recombination reaction of water molecules, temperature effects, and Joule heating. The VAC is built and analyzed.

Discussion and Conclusions. The transport of binary salt ions through a diffusion layer near a cation exchange membrane is considered. A mathematical model of this process is proposed. It takes into account the temperature effects due to dissociation/recombination reactions of water molecules and Joule heating in a solution. The basic laws of the transport of salt ions are established considering the dissociation/recombination reaction of water molecules and temperature effects. The temperature effects of the dissociation/recombination reaction and the Joule heating in the electroneutrality region (ENR) are almost imperceptible (with the exception of the recombination region, RR). The Joule heating in the space-charge region (SCR) is by two orders of magnitude larger than the cooling effect of the water dissociation reaction. Upon recombination, approximately the same heat is released in the RR as during Joule heating in the expanded SCR. However, due to the small size of the RR, the effect of this heat is imperceptible. Therefore, we can assume that there is only one heat source at the interface in the SCR, which, due to its noticeable size, causes a significant increase in temperature in the entire diffusion layer. It follows that the emergence and development of gravitational convection is possible. General conclusions, following from the results obtained, open up the possibility of intensifying the process of transport of salt ions in the electrodialysis machines.

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